Showing papers on "Stress concentration published in 2003"

Mechanical behavior of materials

Abstract: Chapter 1. Introduction.1.1 Strain1.2 Stress.1.3 Mechanical Testing.1.4 Mechanical Responses to Deformation.1.5 How Bonding Influences Mechanical Properties.1.6 Further Reading and References.1.7 Problems.Chapter 2. Tensors and Elasticity.2.1 What Is a Tensor?2.2 Transformation of Tensors.2.3 The Second Rank Tensors of Strain and Stress.2.4 Directional Properties.2.5 Elasticity.2.6 Effective Properties of Materials: Oriented Polycrystals and Composites.2.7 Matrix Methods for Elasticity Tensors.2.8 Appendix: The Stereographic Projection.2.9 References.2.10 Problems.Chapter 3. Plasticity.3.1 Continuum Models for Shear Deformation of Isotropic Ductile Materials.3.2 Shear Deformation of Crystalline Materials.3.3 Necking and Instability.3.4 Shear Deformation of Non Crystalline materials.3.5 Dilatant Deformation of Materials.3.6 Appendix: Independent Slip Systems.3.7 References.3.8 Problems.Chapter 4. Dislocations in Crystals.4.1 Dislocation Theory.4.2 Specification of Dislocation Character.4.3 Dislocation Motion.4.4 Dislocation Content in Crystals and Polycrystals.4.5 Dislocations and Dislocation Motion in Specific Crystal Structures.4.6 References.4.7 Problems.Chapter 5. Strengthening Mechanisms.5.1 Constraint Based Strengthening.5.2 Strengthening Mechanisms in Crystalline Materials.5.3 Orientation Strengthening.5.4 References.5.5 Problems.Chapter 6. High Temperature and Rate Dependent Deformation.6.1 Creep.6.2 Extrapolation Approaches for Failure and Creep.6.3 Stress Relaxation.6.4 Creep and Relaxation Mechanisms in Crystalline Materials.6.5 References.6.6 Problems.Chapter 7. Fracture of Materials.7.1 Stress Distributions Near Crack Tips.7.2 Fracture Toughness Testing.7.3 Failure Probability and Weibull Statistics.7.4 Mechanisms for Toughness Enhancement of Brittle Materials.7.5 Appendix A: Derivation of the Stress Concentration at a Through Hole.7.6 Appendix B: Stress Volume Integral Approach for Weibull Statistics.7.7 References.7.8 Problems.Chapter 8. Mapping Strategies for Understanding Mechanical Properties.8.1 Deformation Mechanism Maps.8.2 Fracture Mechanism Maps.8.3 Mechanical Design Maps.8.4 References.8.5 Problems.Chapter 9. Degradation Processes: Fatigue and Wear.9.1 Cystic Fatigue of materials.9.2 Engineering Fatigue Analysis.9.3 Wear, Friction, and Lubrication.9.4 References.9.5 Problems.Chapter 10. Deformation Processing.10.1 Ideal Energy Approach for Modeling of a Forming Process.10.2 Inclusion of Friction and Die Geometry in Deformation Processes: Slab Analysis.10.3 Upper Bound Analysis.10.4 Slip Line Field Analysis.10.5 Formation of Aluminum Beverage Cans: Deep Drawing, Ironing, and Shaping.10.6 Forming and Rheology of Glasses and Polymers.10.7 Tape Casting of Ceramic Slurries.10.8 References.10.9 Problems.Index.

Handbook of elasticity solutions

Abstract: 1: Basic Equations of Elasticity. 1.1. Cartesian Coordinates. 1.2. Cylindrical Coordinates. 1.3. Spherical Coordinates. 1.4. Hooke's Law for Anisotropic Materials. 2: Point Forces and Systems of Point Forces in Three-Dimensional Space and Half-Space. 2.1. Point Force in an Infinite Isotropic Solid. 2.2. Systems of Forces Distributed in a Small Volume of an Infinite Isotropic Solid. 2.3. Dynamic Problems of a Suddenly Introduced Point Forces Couples and Dipoles in an Infinite Isotropic Solid. 2.4. Point Force in the Isotropic Half-Space (Mindlin's Problem). 2.5. Point Force Applied at the Boundary of the Isotropic Half-Space. 2.6. Point Force of an Infinite Transverse Isotropic Solid. 2.7. Point Force Applied at the Boundary of the Transversely Isotropic Half-Space. 2.8. Two Joined Isotropic Half-Spaces with Different Moduli: Solution for a Point Force. 3: Selected Two-Dimensional Problems. 3.1. Introductory Material. 3.2. Infinite 2-D Solid. Isotropic and Orthotropic Materials. 3.3. 2-D Isotropic Half-Plane. 3.4. Stress Concentrations near Holes and Inclusions. 3.5. Equilibrium of an Elastic Wedge. 3.6. Circular Ring Loaded by External and Internal Pressures. 4: Three-Dimensional Crack Problems for the Isotropic or Transversely Isotropic Infinite Solid. 4.1. Circular (Penny-Shaped) Crack. 4.2. Half-Plane Crack. 4.3. External Circular Crack. 4.4. Elliptical Crack. 5: A Crack in an Infinite Isotropic Two-Dimensional Solid. 5.1. A Pair of Equal and Opposite Point Forces Applied at an Arbitrary Pointof the Crack. 5.2. Uniform Loading at Crack Faces. 5.3. Crack Tip Fields. 5.4. Far Field Asymptotics. 6: A Crack in an Infinite Anisotropic Two-Dimensional Solid. 6.1. Notations and General Representations for a 2-D Anisotropic Elastic Solid. 6.2. A Pair of Equal and Opposite Point Forces Applied at an Arbitrary Point of the Crack. 6.3. Uniform Loading at Crack Faces. 6.4. Crack Tip Fields. 6.5. Far Field Asymptotics. 6.6. Crack Compliance Tensor. 6.7. Appendix. 7: Thermoelasticity. 7.1. Basic Equations. 7.2. Stationary 3-D Problems. 7.3. Non-Stationary 3-D Problems. 7.4. Stationary 2-D Problems. 7.5. Non-Stationary 2-D Problems. 7.6. Thermal Stresses in Heated Infinite Solid Containing an Inhomogeneity or a Cavity. 8: Contact Problems. 8.1. 2-D Problems for a Rigid Punch on the Isotropic and Anisotropic Elastic Half-Plane. 8.2. 3-D Problems for a Rigid Punch on the Isotropic and Transversely Isotropic Elastic Half-Space. 8.3. Contact of Two Elastic Bodies (Hertz' Problem). 9: Eshelby's Problem and Related Results. 9.1. Inclusion Problem. 9.2. Ellipsoidal Inhomogeneity. 9.3. Eshelby's Tensor for Various Ellipsoidal Shapes. 9.4. Alternative Form of Solution for Ellipsoidal Inhomogeneity. 9.5. Expressions for Tensors P, Q, A and GBPIiGBP. 9.6. Quantities Relevant for Calculation of the Effective Elastic Properties. 10: Elastic Space Containing a Rigid Ellipsoidal Inclusion Subjected to Translation and Rotation. 10.1.

Review of the fatigue assessment of welded joints by local approaches

Abstract: The local approach is one of the most important method developed in recent years for fatigue assessment of welded joints. The basic principle of local approach is taking the “local parameter" of the stress concentration region as a characteristic parameter to describe the fatigue behavior and to establish the general S—N curves expressed by the correlate local parameters and the loading cycles N which lead to the prediction of fatigue life and strength of welded components possible. The local approaches could effectively represent the practical fatigue performances of welded structures due to the inclusion of the local geometrical details of the welded joints. This method is recommended by the International Institute of Welding (IIW) and widely employed by various societies in Europe. Various local fatigue criteria for fatigue assessment are developed in recent years, such as notch stress intensity factor (N-SIF), equivalent stress intensity factor (E-SIF), critical distance method (CMD) which includes point method (PM), line method (LM), area method (AM) and volumetric method (VM). The principles, procedures and effect factors about the local approaches are discussed in this paper.

Influence of interfacial intermetallic compound on fracture behavior of solder joints

Abstract: This paper studies the solder joints of an Sn–Ag lead-free solder system with pure copper wires. The study focuses upon the interrelationships, which exist between the adhesive strength of the joint, its shear strength, the formation of interfacial intermetallic compounds (IMC) and the fractographic morphology. Additionally, the paper determines how these characteristics, and the relationships between them, are influenced by the storage duration and the storage temperature. Experimental results show that both the adhesive strength and the shear strength of the solder joints decrease significantly following short-term thermal storage. As the storage time is increased, it is noted that both the thickness and the roughness of the interfacial IMC layers increase. Regarding the fracture of the solder joints, fractographic observation reveals that fracture morphology under adhesive loading are similar to those observed under shear loading conditions. In the as-soldered condition, the fracture surface appears to be flat, and some broken Cu6Sn5 and residual solder pieces are evident. When the total thickness of the IMC layer lies within the range 1–10 μm, it is observed that the fracture morphology gradually becomes a dimple-like structure. This phenomenon may be attributed to the residual stresses caused by phase transformation, and by the increasing roughness of the IMC layers which causes an increase in the stress concentration within the Cu6Sn5 layer, and which ultimately results in fracturing of this layer. When the total thickness of the interfacial IMC layers exceeds 10 μm, the roughness of the IMC layers and the residual stress between them and the solder both continue to increase. Eventually this results in a fracture being initiated and propagated within the Cu6Sn5 layer. Fractographic observation shows the fracture to have a cleavage-like morphology.

Defect analysis in thermal nanoimprint lithography

Abstract: The fracture defect of the polymer in thermal nanoimprint lithography is studied based on numerical simulation and experiments. Hot pressing, cooling, and releasing steps in nanoimprint lithography are investigated in detail by a numerical simulation study. The applied pressure after the polymer deformation below the glass transition temperature will induce a stress concentration at the corner of the polymer pattern. On the other hand, the difference of the thermal expansion coefficients between the mold and the substrate causes lateral strain, and the strain is concentrated at the corner of the pattern. These strains induce defects and cause fracture defects at the base part of the pattern during the mold releasing step. To eliminate the defects, the applied pressure is released below the glass transition temperature, and slow cooling is introduced to relax the stress concentration. The result shows successful fabrication of fine patterns with a high aspect ratio.

The mechanical strength of polysilicon films: Part 2. Size effects associated with elliptical and circular perforations

Abstract: A systematic study of failure initiation in small-scale specimens has been performed to assess the effect of size scale on “failure properties” by drawing on the classical analysis of elliptically perforated specimens. Limitations imposed by photolithography restricted the minimum radii of curvature of the specimen perforations to one micron. By varying the radius of curvature and the size of the ellipses, the effects of domain size and stress concentration amplitude could be assessed separately to the point where the size of individual grains (∼0.3 μm ) becomes important. The measurements demonstrate a strong influence of the domain size under elevated stress on the “failure strength” of MEMS scale specimens, while the amplitude, or the variation, of the stress concentration factor is less significant. In agreement with probabilistic considerations of failure, the “local failure strength” at the root of a notch clearly increases as the radius of curvature becomes smaller. Accordingly, the statistical scatter also increases with decreasing size of the (super)stressed domain. When the notch radius becomes as small as 1 μm the failure stress increases on average by a factor of two relative to the tension values derived from unnotched specimens. This effect becomes moderate for larger radii of curvature, up to a radius of 8 μm (25 times the grain size), for which the failure stress at the notch tip closely approaches the value of the tensile strength for un-notched tensile configurations. We deduce that standard tests, performed on micron-sized, non-perforated, tension specimens, provide conservative strength values for design purposes. In addition, a Weibull analysis shows for surface-micromachined specimens a dependence of the strength on the specimen length, rather than the surface area or volume, which implies that the sidewall geometry, dimensions and surface conditions can dominate the failure process.

Multiscale modeling of carbon nanotube reinforced polymer composites.

Abstract: This article examines the effect of interfacial load transfer on the stress distribution in carbon nanotube/polymer composites through a stress analysis of the nanotube/matrix system. Both isostrain and isostress loading conditions are investigated. The nanotube is modeled by the molecular structural mechanics method at the atomistic level. The matrix is modeled by the finite element method, and the nanotube/matrix interface is assumed to be bonded either perfectly or by van der Waals interactions. The fundamental issues examined include the interfacial shear stress distribution, stress concentration in the matrix in the vicinity of nanotube ends, axial stress profile in the nanotube, and the effect of nanotube aspect ratio on load transfer.

Cyclic testing of built-up steel shear links for the new bay bridge

Abstract: Tests were conducted on two prototype steel shear links for the main tower of the new San Francisco-Oakland Bay self-anchored suspension bridge to evaluate the link force and deformation capacities. The links were built-up wide-flange sections, designed to yield in shear. A quasi-static loading protocol was used to test the links in reverse curvature, simulating the expected seismic demand. The link capacities exceeded the predicted demands from the Safety Evaluation Earthquake. The specimens behaved in a ductile manner until small cracks initiated at the end of the vertical fillet welds connecting the intermediate stiffeners to the link web. As the cracks propagated further, brittle fracture of the web ensued. The maximum shear strength was nearly twice the expected yield shear strength, a significantly higher overstrength than current codes recognize. Alleviating the stress concentration on the vertical fillet welds of the intermediate web stiffeners is necessary to avoid brittle fracture and to increas...

Polarization-sensitive optical coherence tomography for photoelasticity testing of glass/epoxy composites.

Abstract: We measure the spatial distribution of the mechanical stress induced inside translucent glass/epoxy composites by means of polarization-sensitive optical coherence tomography. The Stokes parameters determined from two orthogonal polarization components of the backscattered light allow the internal stress to be identified in terms of its magnitude and principal direction based on a birefringence light scattering model of glass/epoxy composites. Measurement examples show the particular case of stress concentration near a through hole and the internal structural damages caused by excessive tensile loading.

Stress analysis of an upper central incisor restored with different posts.

Abstract: The effect of different anatomic shapes and materials of posts in the stress distribution on an endodontically treated incisor was evaluated in this work. This study compared three post shapes (tapered, cylindrical and two-stage cylindrical) made of three different materials (stainless steel, titanium and carbon fibre on Bisphenol A-Glycidyl Methacrylate (Bis-GMA) matrix). Two-dimensional stress analysis was performed using the Finite Element Method. A static load of 100N was applied at 45 degrees inclination with respect to the incisor's edge. The stress concentrations did not significantly affect the region adjacent to the alveolar bone crest at the palatine portion of the tooth, regardless of the post shape or material. However, stress concentrations on the post/dentin interface on the palatine side of the tooth root presented significant variations for different post shapes and materials. Post shapes had relatively small impact on the stress concentrations while post materials introduced higher variations on them. Stainless steel posts presented the highest level of stress concentration, followed by titanium and carbon/Bis-GMA posts.

Fracture strength of polysilicon at stress concentrations

Abstract: Mechanical design of MEMS requires the ability to predict the strength of load-carrying components with stress concentrations. The majority of these microdevices are made of brittle materials such as polysilicon, which exhibit higher fracture strengths when smaller volumes or areas are involved. A review of the literature shows that the fracture strength of polysilicon increases as tensile specimens get smaller. Very limited results show that fracture strengths at stress concentrations are larger. This paper examines the capability of Weibull statistics to predict such localized strengths and proposes a methodology for design. Fracture loads were measured for three shapes of polysilicon tensile specimens - with uniform cross-section, with a central hole, and with symmetric double notches. All specimens were 3.5 /spl mu/m thick with gross widths of either 20 or 50 /spl mu/m. A total of 226 measurements were made to generate statistically significant information. Local stresses were computed at the stress concentrations, and the fracture strengths there were approximately 90% larger than would be predicted if there were no size effect (2600 MPa versus 1400 MPa). Predictions based on mean values are inadequate, but Weibull statistics are quite successful. One can predict the fracture strength of the four shapes with stress concentrations to within /spl plusmn/10% from the fracture strengths of the smooth uniaxial specimens. The specimens and test methods are described and the Weibull approach is reviewed and summarized. The CARES/Life probabilistic reliability program developed by NASA and a finite element analysis of the stress concentrations are required for complete analysis. Incorporating all this into a design methodology shows that one can take "baseline" material properties from uniaxial tensile tests and predict the overall strength of complicated components. This is commensurate with traditional mechanical design, but with the addition of Weibull statistics.

On the Self-Healing Fracture Mode

Abstract: We present the analytical solution for a fundamental fracture mode in the form of a self-similar, self-healing pulse. The existence of such a fracture mode was strongly suggested by recent numerical simulations of seismic ruptures but, to our knowledge, no formal proof of their origin has been proposed yet. We present a two-dimensional, anti-plane solution for fixed rupture and healing speeds that satisfies both the wave equation and crack boundary conditions for a simple Coulomb friction law in the absence of any rate or state dependence. This solution is an alternative to the classic self-similar crack solution by Kostrov. In practice, the self-healing impulsive mode rather than the expanding crack mode is selected depending on details of fracture initiation and is thereafter self-maintained. We discuss stress concentration, fracture energy, and rupture velocity and compare them to the case of a crack. The analytical study is complemented by various numerical examples and comparisons. On more general grounds, we argue that an infinity of marginally stable fracture modes may exist in addition to the crack solution or the impulsive fracture described here. Manuscript received 27 March 2002.

Fatigue crack growth and fracture paths in sand cast B319 and A356 aluminum alloys

Abstract: The effect of heat-treatment on the fatigue crack growth and fracture paths in lost foam sand cast B319 and A356 Al has been examined by in situ testing in a scanning electron microscope. Fatigue crack growth and fracture toughness experiments were performed at ambient temperature on B319 Al in T5, T6, and T7 conditions and on A356 in the T6 condition to characterize the crack path and the interaction of the crack-tip with the microstructure. High-resolution micrographs of the near-tip region were analyzed using a machined-vision-based stereoimaging technique, known as DISMAP, to determine the crack-tip displacement and strain fields. Selected-area energy dispersive spectroscopy was used to identify the particles in the wake of the fatigue cracks, as well as the alloy content of the Al-matrix ahead of the crack-tip. Microhardness tests revealed the presence of hard and soft zones in B319-T6 that the fatigue cracks tended to follow. The fatigue crack growth rate was reduced and the crack path altered when the crack-tip interacted with (1) localized shear bands, (2) interdendritic boundaries, (3) particle/matrix interface, (4) shrinkage pores, and (5) fractured particles. The decrease in the fatigue crack growth rate can be attributed to increasing crack-tip shielding due to crack branching and deflection. The fracture toughness of A356-T6 is higher than the B319 materials because of the absence of shear localization in the matrix.

On the Sensitivity of Wall Stresses in Diseased Arteries to Variable Material Properties

Abstract: Accurate estimates of stress in an atherosclerotic lesion require knowledge of the material properties of its components (e.g., normal wall, fibrous plaque, calcified regions, lipid pools) that can only be approximated. This leads to considerable uncertainty in these computational predictions. A study was conducted to test the sensitivity of predicted levels of stress and strain to the parameter values of plaque used in finite element analysis. Results show that the stresses within the arterial wall, fibrous plaque, calcified plaque, and lipid pool have low sensitivities for variation in the elastic modulus. Even a +/- 50% variation in elastic modulus leads to less than a 10% change in stress at the site of rupture. Sensitivity to variations in elastic modulus is comparable between isotropic nonlinear, isotropic nonlinear with residual strains, and transversely isotropic linear models. Therefore, stress analysis may be used with confidence that uncertainty in the material properties generates relatively small errors in the prediction of wall stresses. Either isotropic nonlinear or anisotropic linear models provide useful estimates, however the predictions in regions of stress concentration (e.g., the site of rupture) are somewhat more sensitive to the specific model used, increasing by up to 30% from the isotropic nonlinear to orthotropic model in the present example. Changes resulting from the introduction of residual stresses are much smaller.

Initiation of fracture at the interface corner of bi-material joints

Abstract: Within the context of linear elasticity, a stress singularity of the form Hr λ −1 may exist at the interface corner of a bi-material joint, where r is the radial distance from the corner, H is the stress intensity factor and λ −1 is the order of the singularity. Recent experimental results in the literature support the use of a critical value of the intensity factor H = H c as a fracture initiation criterion at the interface corner. In this paper, we examine the validity and limitations of this criterion for predicting the onset of fracture in a butt joint consisting of a thin layer of an elastic–plastic adhesive layer sandwiched between two elastic adherends. The evolution of plastic deformation at the corner is determined theoretically and by the finite element method, and the solution is compared with the extent of the elastic singular field. It is shown that H c is a valid fracture parameter if h > B ( H c / σ Y ) 1/(1− λ ) where the non-dimensional constant B =100 for β =0 and B =13 for β = α /4. Here, h is the thickness of the adhesive layer, σ Y is the uniaxial yield stress of the bulk adhesive and ( α , β ) are Dundurs’ parameters (Dundurs, J., J. Appl. Mech. 36 (1969) 650). Experimental results for aluminium/epoxy/aluminium and brass/solder/brass sandwiched joints are used to assess the role of plastic deformation on the validity of the failure criterion.